Ok we can get sharper
f(x) = exp(x) - exp(-x) + (7/10)(exp(- 5/4 x) - exp(- 9/4 x))
f(x) = (27 x)/10 - (49 x^2)/40 + (459 x^3)/320 - (2597 x^4)/3840 + (34329 x^5)/102400 + O(x^6)
(Taylor series)
This f(x) is periodic with 8 pi i, and bijective on R
and f'(0) = 2.7 what is close to e.
regards
tommy1729
f(x) = exp(x) - exp(-x) + (7/10)(exp(- 5/4 x) - exp(- 9/4 x))
f(x) = (27 x)/10 - (49 x^2)/40 + (459 x^3)/320 - (2597 x^4)/3840 + (34329 x^5)/102400 + O(x^6)
(Taylor series)
This f(x) is periodic with 8 pi i, and bijective on R
and f'(0) = 2.7 what is close to e.
regards
tommy1729